There are generally two ways they are held in place. Some buttons have an "eye" on the back of them and are held in place with button twine attached on the back of the seat cover with a slip knot.
Other buttons have a threaded or smooth nail that is held in place on the back of the seat cover with a spring steel washer.
Buttons with eyes are the easiest to repair without taking the seat cover off, but with a threaded or smooth nail, you will have to take the seat cover off to remove the spring washer from the button.
No one lives forever, the trick is creating something that will.